I have a waterlogged ear. How do I get the water out other than shaking my head while pulling my ear?

Ear. you need to see an ent to have your ear examined. No OTC rx will work unfortunately.
Try Valsalva. Try valsalva maneuver - take a mouthful of air, while clipping your nostrils with your hand and strain like you are about to have a bowel movement. This maneuver opens the eustacian tube and may help get the fluid behind the ear drum. The water in the canal should just get out of there with time. If you have a wax plug, this needs to be removed by doctor if is not able to come out on its own.